Good question, looking forward to answers. But your last question is trivial if you know what scalar and vector field is. Namely, they are fields transforming as spin 0 and spin 1 representations of the Lorentz group. These numbers actually correspond to number of tensor indices of the field, so it shouldn't be surprising that metric as a rank two tensor is associated with spin 2 particles. There is some more math relating to group theory involved (and also some subtleties because of the masslessness) but this is the basic reason.
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MarekFeb 20 '11 at 15:16

@Marek , sorry I haven't (yet) studied group theory. I can understand what are you saying because the scalar field has not elicity and polarizations, and a vectorial field has 3 components and I can connect to them 3 polarization and the field has elicity. but the electromagnetic field is a tensor too $F^{\mu\nu}$, we quantize the vectorial field potential $A^\mu$ don't we? And for a tensorial field like gravity what are elicities?
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Boy SimoneFeb 20 '11 at 15:26

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it's a little bit more complicated than that. EM field has only 2 physical polarizations (the transverse ones) because it is massless. Massive vector field would also have a longitudinal polarization (for a total of 3) but again one polarization is unphysical. As for tensor fields there are more options. It depends on what kind of tensor we are talking about (e.g. whether it is symmetric, traceless, and so on) and again also whether it is massive. But in general when something is massless it has has only two helicities (the left- and right-handed ones).
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MarekFeb 20 '11 at 15:33

I've bean using EM based quantum formula(Braket, Expectation and Operators) for some time. I still feel uncomfortable using it, as compared with other forms of mathematical methods. I think if I got a chance to see its application with other forces (other than EM), I might get a better understanding of how it operates. Even if the final formulas show an unattainable solution, I like this question, and always appreciate a good demonstration.
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Luke BurgessDec 10 '13 at 20:10

1 Answer
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Spin 2 just means that the gravitational field is given by a metric field and general covariance, which is the nonlinear expression of a massless spin 2 representation of the Poincare group. The latter appears when linearizing around the Minkowski metric and dropping all interactions.

Abstract: We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.

-1; i) completely inaccessible link for a person who is beginning to study second quantization. ii) obscure and imprecise explanation of the reason for graviton being a spin-2 particle.
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Arash ArabiDec 12 '13 at 6:41

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@ArashArabi: Criticising is easy. Be constructive, and post a clearer and more precise explanation of the reason for the graviton being a spin-2 particle!
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Arnold NeumaierDec 13 '13 at 9:30

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Oh Arnold, it is good to see you back.
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Jia YiyangDec 13 '13 at 13:09

@ArnoldNeumaier I will try Arnold. Also, I did not mean to say your answer was not helpful; it was just not helpful enough for a beginner. The edit made it certainly better though, in my opinion.
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Arash ArabiDec 13 '13 at 23:50